How to change the shadow color in Blender Cycles?
With the Cycles renderer enabled select the cube, give it a new material and set the material nodes as pictured below. Use the Is Camera Ray of the Light Path node as a factor for mixing the Diffuse and Transparent nodes (Is Shadow Ray works good as well).


Change the Hue, Saturation and Value values of the Transparent shader to change the shadow's color, intensity and transparency.


Here's the animated test using the changes mentioned above: